If you are going to use the white man's burden go all the way.

Lets see some freemarket colonialism.
Rather than himming and hawwing over how much or what type of aid to give this we should just create colonial bids, sellable and transferrable, that would give a corporation the right to meddle in a country however they please.
This can all be handled in the US, other non american NGOs and aid funding is nothing compared to what we put out.
The corporations would of course have to be profitable, and whatever form of power structure in the country would react accordingly.
With this model we could use the market to decide what form of imperialism works.
How the corporations fund this I don't care. Heck if they use the hands off approach it wouldn't cost anything. And maybe the kleptocracies might have to shrink their budgets.
The interventionist companies could however create revenue streams from the charity scene or even collect the natural resources from said countries and build infrastructure in said countries.
Even still, a country that wanted to could buy the rights themselves; assuming google or starbucks wouldn't outbid their 15 coconuts.

The main difficulty with this method would be how the sovereign states would react. It is likely that it would sadly continue the trend of poor and authorutarian countries having very little in the form of aid reach their populace. I have my doubts that the bid to help Burma would be terribly expensive.
This wouldn't necessarily be completely limiting though. I imagine a large enough corporation can afford decent secuirity. Even if said secuirity is a small army and a number of special forces platoons.
There are plenty of poor countries bursting at the seams as far as natural resources can be considered. This is reason enough to believe that companies would be willing to spend the money to interfere.
As an example one could look to the Iraq war. Plenty of value to be gained from that oil in the ground. Shame the US couldn't handle the job of getting it out without wasting the country. Perhaps the market could handle something like that better.

Add cost sensitivity to the right of imperialism and we might just get a system that does more good than bad.